Mixture of experts architectures for neural networks as a special case of conditional expectation formula.

*(English)*Zbl 1274.68314Summary: Recently a new interesting architecture of neural networks called “mixture of experts” has been proposed as a tool of real multivariate approximation or prediction. We show that the underlying problem is closely related to approximating the joint probability density of involved variables by finite mixture. Particularly, assuming normal mixtures, we can explicitly write the conditional expectation formula which can be interpreted as a mixture-of-experts network. In this way the related optimization problem can be reduced to standard estimation of normal mixtures by means of EM algorithm. The resulting prediction is optimal in the sense of minimum dispersion if the assumed mixture model is true. It is shown that some of the recently published results can be obtained by specifying the normal components of mixtures in a special form.

##### MSC:

68T05 | Learning and adaptive systems in artificial intelligence |

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[1] | Dempster A. P., Laird N. M., Rubin D. B.: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. ser. B 39 (1977), 1-38 · Zbl 0364.62022 |

[2] | Grim J.: On numerical evaluation of maximum-likelihood estimates for finite mixtures of distributions. Kybernetika 18 (1982), 3, 173-190 · Zbl 0489.62028 |

[3] | Grim J.: Maximum likelihood design of layered neural networks. IEEE Proceedings of the 13th International Conference on Pattern Recognition, IEEE Press 1996, pp. 85-89 |

[4] | Grim J.: Design of multilayer neural networks by information preserving transforms. Proc. 3rd Systems Science European Congress (E. Pessa, M. B. Penna and A. Montesanto, Edizzioni Kappa, Roma 1996, pp. 977-982 |

[5] | Jacobs R. A., Jordan M. I., Nowlan S. J., Hinton G. E.: Adaptive mixtures of local experts. Neural Comp. 3 (1991), 79-87 |

[6] | Jordan M. I., Jacobs R. A.: Hierarchical mixtures of experts and the EM algorithm. Neural Comp. 6 (1994), 181-214 |

[7] | Chen, Ke, Xie, Dahong, Chi, Huisheng: A modified HME architecture for text-dependent speaker identification. IEEE Trans. Neural Networks 7 (1996), 1309-1313 |

[8] | Ramamurti V., Ghosh J.: Structural adaptation in mixtures of experts. IEEE Proceedings of the 13th International Conference on Pattern Recognition, IEEE Press, 1996, pp. 704-708 |

[9] | Titterington D. M., Smith A. F. M., Makov U. E.: Statistical Analysis of Finite Mixture Distributions. John Wiley & Sons, Chichester - Singapore - New York 1985 · Zbl 0646.62013 |

[10] | Vajda I.: Theory of Statistical Inference and Information. Kluwer, Boston 1992 · Zbl 0711.62002 |

[11] | Wu C. F. J.: On the convergence properties of the EM algorithm. Ann. Statist. 11 (1983), 95-103 · Zbl 0517.62035 |

[12] | Xu L., Jordan M. I.: On convergence properties of the EM algorithm for Gaussian mixtures. Neural Comp. 8 (1996), 129-151 · Zbl 05476078 |

[13] | Xu L., Jordan M. I., Hinton G. E.: A modified gating network for the mixtures of experts architecture. Proc. WCNN’94, San Diego 1994, Vol. 2, pp. 405-410 |

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